k spring constant
of the beam in N/marea overlapping area of the
electrodes in µm2m inertial mass in kggap distance between the
stationary and movable plate in µm volt applied voltage in Voltg
amplitude of the pulse signal in gnp
number of active stationary plates, 1 plate by defaultrper relative permittivity of the medium, it is
approximately 1 for airsel number denoting the
selected result.
Use 2 for maximum time duration of pulse

Notes

This interface could be used for designing a capacitive accelerometer meant to
sense or operate under a pulse signal. Pulse signal has a large amplitude of acceleration
acting for a very short period of time. Pulse signals are usually the worst
form of shock loads that the accelerometer will face during operation and
hence should be designed to survive this kind of load. For any given magnitude
of acceleration a corresponding maximum value for the pulse duration can be
found out.

The accelerometer has a mass suspended from a beam with a known spring
constant. The stationary electrode can be one or two as shown in the figure
above. For capacitance measurement an electrical excitation is applied between
the stationary and movable electrodes. This electrical excitation also exerts
an electrostatic attraction on the mass which has the movable electrode. The
combination of the electrostatic force and the inertial force should not be
large enough to send the mass into a pulled-in state where the mass hits one
of the stationary electrodes. For single sided excitation, the mass has an
offset from the equilibrium position due to the electrical excitation. For
double sided excitation, this effect is cancelled off.

The capacitor
design or the applied voltage can be changed to increase the range
of operation. The applied voltage usually has a AC component and a DC
component typically in the form of ±V1±V2sinωt
where frequency ω is much larger than the
frequency of the signal and the natural frequency of vibration of the
accelerometer. The effective applied voltage can be expressed as

V = √(V12
+ V22∕2)

The plot shows acceleration measured in terms of acceleration due
to gravity g versus the maximum pulse time in µsec. The plot shows that the
allowable pulse duration drops off rapidly with the magnitude of acceleration. A
pulse duration above this maximum value can make the system unstable. It
can also be seen that for double sided excitation, the operational range is
larger than for single sided excitation. For the same accelerometer and supply
voltage, the maximum allowable acceleration or pulse duration is slightly
higher for double sided excitation.

Assumptions

-Pulse acceleration signal normal to the plane of the mass is assumed.-Damping effects are not considered.
-The pulse duration is small and the magnitude of acceleration is large-The stationary electrodes are arranged symmetrically on both sides of the
movable electrode.
-The spring constant of the beam is known. If unknown, this can be calculated
under Mechanics > Structures > Beams.-The medium between the electrodes is
air by default with a relative permittivity of 1. -The gap between the
electrodes is uniform.-The supply voltage is constant.-The static displacement of the mass before the
application of voltage and acceleration signal is considered to be zero.